local using ''Coordinate System Manager''. Can someone helps ?

I have created a local site using ''Coordinate System Manager''. That site has a local GEOID that I have added to the new local site.I attached the local site step-by-step creation screenshot.

Though when I enter a Grid coordinate, the Ellipsoid Height that TBC gives me is different from the one the customer has as Ellipsoid Height. Same issue when I enter a local coordinates, the elevation of TBC doesn't match with the one of the customer. The difference is about 5 cm.